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We utilize a nuclear shell model Hamiltonian with only two adjustable parameters to generate, for the first time, exact solutions for pairing correlations for light to medium-mass nuclei, including the challenging proton-neutron pairs, while also identifying the primary physics involved. In addition to single-particle energy and Coulomb potential terms, the shell model Hamiltonian consists of an isovector T=1 pairing interaction and an average proton-neutron isoscalar T=0 interaction, where the T=0 term describes the average interaction between nonpaired protons and neutrons. This Hamiltonian is exactly solvable, where, utilizing three to seven single-particle energy levels, we reproduce experimental data for 0+ state energies for isotopes with mass A=10 through A=62 exceptionally well including isotopes from He to Ge. Additionally, we isolate effects due to like-particle and proton-neutron pairing, provide estimates for the total and proton-neutron pairing gaps, and reproduce N (neutron) = Z (proton) irregularity. These results provide a further understanding for the key role of proton-neutron pairing correlations in nuclei, which is especially important for waiting-point nuclei on the rp path of nucleosynthesis.

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Physical Review C